{
  "metadata": {
    "language_info": {
      "codemirror_mode": {
        "name": "python",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.8"
    },
    "kernelspec": {
      "name": "python",
      "display_name": "Pyolite",
      "language": "python"
    },
    "colab": {
      "name": "8.ipynb",
      "provenance": []
    }
  },
  "nbformat_minor": 0,
  "nbformat": 4,
  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "Residual Analysis with Autocorrelation\n",
        "\n",
        "残差分析与自相关"
      ],
      "metadata": {
        "id": "k6zCOZIY5Q2g"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "This example shows how to use autocorrelation with a confidence interval to analyze the residuals of a least-squares fit to noisy data. The residuals are the differences between the fitted model and the data. In a signal-plus-white noise model, if you have a good fit for the signal, the residuals should be white noise.\n",
        "\n",
        "本用例展示了如何使用自相关于置信区间分析残差的最小二乘拟合噪声数据。残差是拟合模型与数据之间的差值。在信号+白噪声的模型当中，如果对信号有较好的拟合，残差应该是白噪声。"
      ],
      "metadata": {
        "id": "cRHQ-V7dRChg"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Create a noisy data set consisting of a 1st-order polynomial (straight line) in additive white Gaussian noise. The additive noise is a sequence of uncorrelated random variables following a N(0,1) distribution. This means that all the random variables have mean zero and unit variance. Set the random number generator to the default settings for reproducible results.\n",
        "\n",
        "在加性高斯白噪声中创建一阶多项式（直线）所组成的噪声数据及。加性噪声是一个不相关的随机变量序列，遵循N(0,1)分布，这意味着所有随机变量的均值为0，方差为1，将随机数生成及设置为可重现结果的默认设置。"
      ],
      "metadata": {
        "id": "GME0nony5Q2j"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "from matplotlib import pyplot as plt\n",
        "from scipy.special import erfcinv\n",
        "from scipy.fft import fft"
      ],
      "metadata": {
        "trusted": true,
        "id": "bpuaEVAg5Q2j"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "x = np.arange(-3, 3, 0.01)\n",
        "y = 2 * x + np.random.randn(len(x))\n",
        "plt.plot(x, y)\n",
        "plt.show()"
      ],
      "metadata": {
        "trusted": true,
        "id": "35y2bf405Q2k",
        "outputId": "3541eda9-4191-449c-a6d1-a8d941075ac2"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": "<pyolite.display.Image at 0x119c248>",
            "image/png": 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"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Use function to find the least-squares line for the noisy data. Plot the original data along with the least-squares fit.\n",
        "\n",
        "使用函数找到噪声数据的最小二乘拟合线，用最小二乘法拟合原始数据。"
      ],
      "metadata": {
        "id": "v26cpTQU5Q2l"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def linearRegression(x, y):\n",
        "    length = len(x)\n",
        "    mx = x.mean()\n",
        "    a =  a = (y * (x - mx)).sum() / ((x ** 2).sum() - x.sum() ** 2 / length)\n",
        "    b = (y - a * x).sum() / length\n",
        "    return a, b"
      ],
      "metadata": {
        "trusted": true,
        "id": "zBISEAKV5Q2l"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "a, b = linearRegression(x, y)\n",
        "yfit = a * x + b\n",
        "\n",
        "plt.plot(x, y, 'b')\n",
        "plt.plot(x, yfit, 'r')\n",
        "plt.show()"
      ],
      "metadata": {
        "trusted": true,
        "id": "cOTwt3eE5Q2l",
        "outputId": "5820e864-7211-4fa3-8e00-b729d6bc8b02"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": "<pyolite.display.Image at 0x3d30e48>",
            "image/png": 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"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Find the residuals. Obtain the autocorrelation sequence of the residuals to lag 50.\n",
        "\n",
        "得到残差，求取滞后值为50的残差自相关序列。"
      ],
      "metadata": {
        "id": "LhVFUMjo5Q2l"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def autocorrelation(x, lags):\n",
        "    n = len(x)\n",
        "    x = np.array(x)\n",
        "    result = [np.correlate(x[i:],x[:n-i])\\\n",
        "            /(x[i:].std()*x[:n-i].std()*(n-i)) for i in range(0, lags+1)]\n",
        "    lag = np.arange(0, lags+1, 1)\n",
        "    return result, lag"
      ],
      "metadata": {
        "trusted": true,
        "id": "0NxeIk3w5Q2m"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "residuals = y - yfit\n",
        "xc,lags = autocorrelation(residuals, 50);"
      ],
      "metadata": {
        "trusted": true,
        "id": "4k_eAsS25Q2m"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "When you inspect the autocorrelation sequence, you want to determine whether or not there is evidence of autocorrelation. In other words, you want to determine whether the sample autocorrelation sequence looks like the autocorrelation sequence of white noise. If the autocorrelation sequence of the residuals looks like the autocorrelation of a white noise process, you are confident that none of the signal has escaped your fit and ended up in the residuals. In this example, use a 99%-confidence interval. To construct the confidence interval, you need to know the distribution of the sample autocorrelation values. You also need to find the critical values on the appropriate distribution between which lie 0.99 of the probability. Because the distribution in this case is Gaussian, you can use complementary inverse error function, erfcinv. The relationship between this function and the inverse of the Gaussian cumulative distribution function is described on the reference page for erfcinv.\n",
        "\n",
        "当检视自相关序列时，如何确认是否存在自相关关系。换言之，如何确定样本自相关序列是否是白噪声的自相关序列，如果残差的自相关序列看起来像是白噪声过程的自相关，确认所有的信号都符合拟合结果，最终表现在残差当中。在本例当中，使用99%的置信区间。为了构造置信区间，需要获取样本自相关值的分布。还需要在概率99%的适当分布中找到临界值，因为示例情况中的分布为高斯分布，可以使用互补逆误差函数。该函数与高斯累积分布函数的逆函数之间的关系可用函数erfcinv描述。"
      ],
      "metadata": {
        "id": "RTSxwfs-T7Wv"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Find the critical value for the 99%-confidence interval. Use the critical value to construct the lower and upper confidence bounds.\n",
        "\n",
        "获取99%置信区间的临界值，使用临界值来构造置信上下限。"
      ],
      "metadata": {
        "id": "MDOnnNwj5Q2m"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "conf99 = np.sqrt(2) * erfcinv(0.01)\n",
        "lconf = -conf99 / np.sqrt(len(x))\n",
        "hconf = conf99 / np.sqrt(len(x))\n",
        "lline = lconf * np.ones(len(lags))\n",
        "hline = hconf * np.ones(len(lags))"
      ],
      "metadata": {
        "trusted": true,
        "id": "hufIKRdp5Q2n"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Plot the autocorrelation sequence along with the 99%-confidence intervals.\n",
        "\n",
        "绘制自相关序列以及99%置信区间。  "
      ],
      "metadata": {
        "id": "I2OWl4Ar5Q2n"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "plt.stem(lags, xc)\n",
        "plt.ylim([lconf-0.03, 1.05])\n",
        "plt.plot(lags, lline, 'r')\n",
        "plt.plot(lags, hline, 'r')\n",
        "plt.title('Sample Autocorrelation with 99% Confidence Intervals')\n",
        "plt.show()"
      ],
      "metadata": {
        "trusted": true,
        "id": "GQlO8b0N5Q2n",
        "outputId": "eb9a8702-ce1d-4cbd-a148-59f90b6b86ca"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": "<pyolite.display.Image at 0x3fe8250>",
            "image/png": 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PPPKIqVmzpvnhhx+cXnP8+PEmMDDQ8SOy6L3r169vjh075pjvzTffNJLM22+/7ZjWo0cPU7t2baf9pDHGqSyV3c+VFgBdKV9pYwArso8o+s5Wr17tNO/3339vJJlnnnnGafrf//53U6tWLafPdeFnLCgoMG3atDG9evUq9lnP/87at29/0eMfcXHoAvZSffr00aZNm3TNNdfoq6++0owZM5SWlqZGjRrprbfecpr3/PEZOTk5Onr0qHr27Kl9+/YpJyfHad7ExESlpKQ4/k9OTpYk9erVS3/4wx+KTd+3b1+xso0ZM8bxt81m05gxY1RQUKD333+/xM9ijNFrr72mAQMGyBijo0ePOh5paWnKycnRtm3byqyPX3/9VWvWrNFNN93kmHbDDTfIZrNp2bJlZS5bUZmZmdqxY4eGDh2qevXqOaa3a9dOffr00bvvvivpXPfHG2+8oQEDBpR41mJRF8y7776rLl26qFu3bo7natWqpdtuu00HDhzQrl27nJZLT08vdczNqFGjnP5fvny5IiIi1KdPH6d6TUpKUq1atZy6cy8UGBjo6J602+06duyYzp49q06dOpX7fZSmqG4yMjKcpt9zzz2SVKzbOzExUd27d3f8HxkZqZYtW5a43p2vaJmPP/5Y0rlu1M6dO6tPnz6OLtXjx49r586dTq9/MW677Tan7rTu3bursLBQP/30U6nLBAQE6Pbbb9f69es1YcIE7dmzR1u3btXAgQMdQwOKzqzt16+f4uLidO+992rlypX66aeftGzZMj344IOqUaOG0xm4bdu21Z49e/Tll19qz549WrFihQICAnTPPffohhtu0J/+9CetXLlS7du3V0JCQrnDM3JzcyVJtWvXdqkuPPX9luT9999XQUGBxo4d6/R9jBs3rti8y5cvV/fu3VW3bl2n7SI1NVWFhYWO9abIoEGDnLrWi8pcVM4jR47o448/1vDhw532k9L/tnN37OdKU175ylLRfURCQoLS0tKcprVo0UIdOnRwGo5QWFioFStWaMCAAU77q/P//u2335STk6Pu3buX+9nr1Kmjb7/9Vnv27Cn3M8E9CIBerHPnzlq5cqV+++03bd68WRMmTNCJEyd04403OoWGjRs3KjU11TFWLTIy0jEI/MIAeOHOKyIiQpLUpEmTEqdfOEYkICBATZs2dZrWokULSSr1el1HjhzR8ePHNX/+fEVGRjo9hg0bJqn8E1uWLl2q33//XX/84x/1448/6scff9SxY8eUnJysl19+ucxlK6rowN6yZctiz7Vq1UpHjx5VXl6ejhw5otzcXLVp06bc1yvttc5/vyIJCQklvk6NGjXUuHFjp2l79uxRTk6OGjZsWKxuT548WW69vvjii2rXrp1jzE1kZKRWrVpVbL1x1U8//aSAgAA1b97caXp0dLTq1KlT7LNeuD5KUt26dcsdvxgVFaVLL73UEfY++eQTde/eXT169NAvv/yiffv2aePGjbLb7ZUOgBeWsehAXF4Zp06dqhEjRmjGjBlq0aKFOnXqpBo1amjEiBGS5BinFxISolWrVql+/fq64YYbFB8fryFDhmjSpEmqV69esfF8ISEh6tSpk6OOP/jgA61du1bTp0/X999/r8GDB2vcuHFasGBBuZe4CQ8PlySdOHHCpbrw1Pdb2ntL0qWXXuo0PTIy0ikcSee2i9WrVxfbJlJTUyUV39+U9x0XBa2ytnV37OdKc7HroFTxfURp+59BgwZp48aN+vnnnyWdG7N8+PBhDRo0yGm+d955R3/6058UEhKievXqKTIyUnPnzi13nzJ16lQdP35cLVq0UNu2bXXfffc5jeeF+/nO6XsWFhQUpM6dO6tz585q0aKFhg0bpuXLl2vy5Mnau3evevfurcsuu0wzZ85UkyZNFBQUpHfffVdPPfWU04BnSaWeVVfa9LJaD1xVVIa//vWvSk9PL3GeorMcS1MU8rp27Vri8/v27XMEU5vNVmK5CwsLXS5zdSqt9S84OLjY2cB2u10NGzYsNQQXncBRksWLF2vo0KG67rrrdN9996lhw4YKDAzUtGnTtHfv3ov/AJLLF4euzHrXrVs3rV+/XqdPn9bWrVs1adIktWnTRnXq1NEnn3yi7777TrVq1dIf//jHCpXdXWUMCgrSCy+8oMcee0w//PCDoqKi1KJFC918883FQlTr1q21c+dO7dq1S7/99psSExMVGhqqu+++Wz179iz1PQoLC3XXXXdp/PjxatSokR555BFdfvnljsBx++236+WXX3b8f6Hw8HDFxsZq586d5VWDE098v5Vht9vVp08f3X///SU+X/SjtYg7yumO/VxpKlO+iu4jStv/DBo0SBMmTNDy5cs1btw4LVu2TBEREbrqqqsc83zyySe65ppr1KNHDz377LOKiYnRJZdcooULF+qVV14ps5w9evTQ3r179eabb2rt2rV64YUX9NRTT2nevHm69dZby/2cqDgCoI8p6mrMzMyUJL399tvKz8/XW2+95fQrsayuv8qw2+3at2+f0w70hx9+kCTH2XsXioyMVO3atVVYWOj4BV4R+/fv12effaYxY8YUOxja7Xb97W9/0yuvvKJ//OMfks79Oi6pa+TC1onSDmJFZyV+//33xZ7bvXu3GjRooJo1ayo0NFTh4eHlHjzj4uJKfa3z3+9iNGvWTO+//766du1a4Us1rFixQk2bNtXKlSud6mLy5MlO81XkTh9xcXGy2+3as2ePo4VTkrKzs3X8+PFKfdYLde/eXQsXLtSSJUtUWFioyy+/XAEBAerWrZsjAF5++eXlXkqkqu9kEhUVpaioKEnnAttHH32k5OTkYi17NptNrVu3dvz/7rvvym63l7nNzJ07VydOnNC9994rSfrll18UGxvreD42NtbRYlOaq6++WvPnz9emTZuchoeUxJPfb0nvLZ1r0Tq/F+LIkSPFWsKaNWumkydPXtT+piRF71fWtl7Z/VxllbYeV2Yfcb6EhAR16dJFS5cu1ZgxY7Ry5Updd911Cg4Odszz2muvKSQkRGvWrHGavnDhQpfeo169eho2bJiGDRumkydPqkePHnr44YcJgFWELmAv9eGHH5b4665oDE5Rl2LRwe38eXNyclze4C7G7NmzHX8bYzR79mxdcskl6t27d4nzBwYG6oYbbtBrr71W4g60vEtqFP1yvf/++3XjjTc6PQYOHKiePXs6/bpt1qyZdu/e7fS6X331lTZu3Oj0umFhYZLOjRU7X0xMjDp06KAXX3zR6bmdO3dq7dq16tevn6Rz3eHXXXed3n777RJvF1b0nfTr10+bN2/Wpk2bHM/l5eVp/vz5io+PV2JiYpmfvywDBw5UYWGhHnnkkWLPnT17tthnO19J684XX3zhVE6p9HoqSVHdPP30007TZ86cKUnq379/ua/hqqKu3ccff1zt2rVzDFvo3r271q9fry1btrjU/VuzZk2XPps7PPnkk8rMzHSMmSvN6dOn9dBDDykmJsZp3Ov5jh07psmTJ+uJJ55QSEiIpHNhs+iHhSR99913io6OLvO97r//ftWsWVO33nqrsrOziz2/d+9ezZo1S5Jnv98Lpaam6pJLLtEzzzzjtM5eWBbp3HaxadMmrVmzpthzx48fL3aHlfJERkaqR48eWrBggQ4ePOj0XFFZKrufq6yia4JeuC5XZh9xoUGDBunzzz/XggULdPTo0WLdv4GBgbLZbE69LQcOHNAbb7xR7mv/+uuvTv/XqlVLzZs3L3Z5IbgPLYBeauzYsTp16pSuv/56XXbZZSooKNBnn32mpUuXKj4+3tGl07dvXwUFBWnAgAG6/fbbdfLkST3//PNq2LCho5XQnUJCQrR69Wqlp6crOTlZ7733nlatWqWJEyeW2d04ffp0ffjhh0pOTtbIkSOVmJioY8eOadu2bXr//fd17NixUpd9+eWX1aFDh2LjFItcc801Gjt2rLZt26aOHTtq+PDhmjlzptLS0jRixAgdPnxY8+bNU+vWrR2D3qVzXR2JiYlaunSpWrRooXr16qlNmzZq06aNnnjiCf35z39WSkqKRowYodOnT+uZZ55RRESE07UC//nPf2rt2rXq2bOnbrvtNrVq1UqZmZlavny5Pv30U9WpU0fjx4/Xq6++qj//+c+68847Va9ePb344ovav3+/XnvttRIv8uyqnj176vbbb9e0adO0Y8cO9e3bV5dccon27Nmj5cuXa9asWU7X6Drf1VdfrZUrV+r6669X//79tX//fs2bN0+JiYk6efKkS/V0ofbt2ys9PV3z58/X8ePH1bNnT23evFkvvviirrvuuhKvJXaxmjdvrujoaH3//fcaO3asY3qPHj30wAMPSJJLATApKUlz587Vo48+qubNm6thw4bq1atXpcu3ePFivfbaa+rRo4dq1aql999/X8uWLdOtt96qG264wWnegQMHKjY2VomJicrNzdWCBQu0b98+rVq1qtQTNB566CG1bdtWf/nLXxzTbrjhBk2dOlWjRo1SXFycnnvuOUc4K02zZs30yiuvaNCgQWrVqpWGDBmiNm3aOPY5y5cvd9yz1ZPf74UiIyN17733atq0abr66qvVr18/bd++Xe+9954aNGjgNO99992nt956S1dffbWGDh2qpKQk5eXl6ZtvvtGKFSt04MCBYsuU59///re6deumjh076rbbblNCQoIOHDigVatWaceOHZIqt5+rrKSkJEnSnXfeqbS0NAUGBmrw4MGV2kdcaODAgbr33nt17733ql69esVaOvv376+ZM2fqqquu0s0336zDhw9rzpw5at68ebnj+RITE3XFFVcoKSlJ9erV05YtW7RixQqnkw7hZh4+6xgueu+998zw4cPNZZddZmrVquW4LdzYsWNNdna207xvvfWWadeunQkJCTHx8fHm8ccfNwsWLCh2uYvSbjMkyYwePdppWkmXZkhPTzc1a9Y0e/fuNX379jVhYWEmKirKTJ482el6gUWveeFlQ7Kzs83o0aNNkyZNzCWXXGKio6NN7969zfz580uth61bt5Z4ncHzHThwwEgyd999t2Pa4sWLTdOmTU1QUJDp0KGDWbNmTbHLwBhz7vpZSUlJJigoqFiZ33//fdO1a1cTGhpqwsPDzYABAxyXHTnfTz/9ZIYMGWIiIyNNcHCwadq0qRk9erTTJVb27t1rbrzxRlOnTh0TEhJiunTpUuy6WEWXgTn/mlpFiuq+NPPnzzdJSUkmNDTU1K5d27Rt29bcf//95pdffnHMc+FlYOx2u/nnP/9p4uLiTHBwsPnjH/9o3nnnnQrVU0nXAfz999/NlClTTEJCgrnkkktMkyZNzIQJE8yZM2ec5ittfazILev+8pe/GElm6dKljmkFBQUmLCzMBAUFFbtNXUmXgcnKyjL9+/c3tWvXNpIc713areCKvqfzL5FUki+++ML06NHD1K1b14SEhJj27dubefPmlXidvscff9xcdtllJiQkxNStW9dcc801jmsxluTrr782QUFBJc6zaNEiEx8fb+rXr28yMjLM2bNnyyxnkR9++MGMHDnSxMfHm6CgIFO7dm3TtWtX88wzzzh9d+7+fl29DIwx5y6vM2XKFBMTE2NCQ0PNFVdcYXbu3FnibcVOnDhhJkyYYJo3b26CgoJMgwYNzOWXX26efPJJx+W0SntvY0reh+3cudNcf/31ju24ZcuWxfZNF7OfK63OKlK+s2fPmrFjx5rIyEhjs9mKbZeu7CNcuRVd165dS7wUUJH//Oc/5tJLLzXBwcHmsssuMwsXLixxP3Hhd/boo4+aLl26mDp16pjQ0FBz2WWXmccee6zES5/BPWzGVPFoXPiNoUOHasWKFU6tQwAAwPcwBhAAAMBiCIAAAAAWQwAEAACwGMYAAgAAWAwtgAAAABZDAAQAALAYAiAAAIDFcCeQSrDb7frll19Uu3btKr+fKAAAcA9jjE6cOKHY2NhK3Y3JlxEAK+GXX34p9fZkAADAux06dEiNGzeu7mJUCwJgJRTdo/PQoUMKDw+v5tIAAABX5ObmqkmTJqXea9sKCICVUNTtGx4eTgAEAMDHWHn4ljU7vgEAACyMAAgAAGAxBEAAAACLIQACAABYDAEQAADAYgiAAAAAFkMABAAAsBiuA+iFCu1Gm/cf0+ETZ9Swdoi6JNRTYIB1r1UEAADcy29aAD/++GMNGDBAsbGxstlseuONN8pd5qOPPlLHjh0VHBys5s2ba9GiRVVezvKs3pmpbo9/oJue/1x3Ldmhm57/XN0e/0Crd2ZWd9EAAICf8JsAmJeXp/bt22vOnDkuzb9//371799fV155pXbs2KFx48bp1ltv1Zo1a6q4pKVbvTNToxZvU2bOGafpWTlnNGrxNkIgAABwC5sxxlR3IdzNZrPp9ddf13XXXVfqPA888IBWrVqlnTt3OqYNHjxYx48f1+rVq116n9zcXEVERCgnJ6fSt4IrtBt1e/yDYuGviE1SdESIPn2gF93BAABUgjuP377Kb1oAK2rTpk1KTU11mpaWlqZNmzaVukx+fr5yc3OdHu6yef+xUsOfJBlJmTlntHn/Mbe9JwAAsCbLBsCsrCxFRUU5TYuKilJubq5Onz5d4jLTpk1TRESE49GkSRO3lefwidLD38XMBwAAUBrLBsCLMWHCBOXk5Dgehw4dcttrN6wd4tb5AAAASmPZy8BER0crOzvbaVp2drbCw8MVGhpa4jLBwcEKDg6ukvJ0SainmIgQZeWcUUmDMovGAHZJqFcl7w8AAKzDsi2AKSkpWr9+vdO0devWKSUlpVrKExhg0+QBiZLOhb3zFf0/eUAiJ4AAAIBK85sAePLkSe3YsUM7duyQdO4yLzt27NDBgwclneu+HTJkiGP+O+64Q/v27dP999+v3bt369lnn9WyZct09913V0fxJUlXtYnR3L92VMNw51bG6IgQzf1rR13VJqaaSgYAAPyJ33QBb9myRVdeeaXj/4yMDElSenq6Fi1apMzMTEcYlKSEhAStWrVKd999t2bNmqXGjRvrhRdeUFpamsfLfr6r2sSoa/MGavvwWknSomGd1f3SSFr+AACA2/jldQA9paquI3Sq4KwSJ527IPWuqWkKC/KbnA4AQLXjOoB+1AUMAAAA1xAAAQAALIYACAAAYDEEQAAAAIshAAIAAFgMARAAAMBiCIAAAAAWQwAEAACwGAIgAACAxRAAAQAALIYACAAAYDEEQAAAAIshAAIAAFgMARAAAMBiCIAAAAAWQwAEAACwGAIgAACAxRAAAQAALIYACAAAYDEEQAAAAIshAAIAAFgMARAAAMBiCIAAAAAWQwAEAACwGAIgAACAxRAAAQAALIYACAAAYDEEQAAAAIshAAIAAFgMARAAAMBiCIAAAAAWQwAEAACwGAIgAACAxRAAAQAALIYACAAAYDEEQAAAAIshAAIAAFgMARAAAMBiCIAAAAAWQwAEAACwGAIgAACAxRAAAQAALIYACAAAYDEEQAAAAIshAAIAAFgMARAAAMBiCIAAAAAWQwAEAACwGAIgAACAxRAAAQAALIYACAAAYDF+FQDnzJmj+Ph4hYSEKDk5WZs3by5z/pdfflnt27dXWFiYYmJiNHz4cP36668eKi0AAED18JsAuHTpUmVkZGjy5Mnatm2b2rdvr7S0NB0+fLjE+Tdu3KghQ4ZoxIgR+vbbb7V8+XJt3rxZI0eO9HDJAQAAPMtvAuDMmTM1cuRIDRs2TImJiZo3b57CwsK0YMGCEufftGmT4uPjdeeddyohIUHdunXT7bffXm6rIQAAgK/ziwBYUFCgrVu3KjU11TEtICBAqamp2rRpU4nLpKSk6NChQ3r33XdljFF2drZWrFihfv36earYAAAA1cIvAuDRo0dVWFioqKgop+lRUVHKysoqcZmuXbvq5Zdf1qBBgxQUFKTo6GhFRERozpw5pb5Pfn6+cnNznR4AAAC+xi8C4MXYtWuX7rrrLk2aNElbt27V6tWrdeDAAd1xxx2lLjNt2jRFREQ4Hk2aNPFgiQEAANzDLwJggwYNFBgYqOzsbKfp2dnZio6OLnGZadOmqWvXrrrvvvvUrl07paWl6dlnn9WCBQuUmZlZ4jITJkxQTk6O43Ho0CG3fxYAAICq5hcBMCgoSElJSVq/fr1jmt1u1/r165WSklLiMqdOnVJAgPPHDwwMlCQZY0pcJjg4WOHh4U4PAAAAX+MXAVCSMjIy9Pzzz+vFF1/Ud999p1GjRikvL0/Dhg2TdK71bsiQIY75BwwYoJUrV2ru3Lnat2+fNm7cqDvvvFNdunRRbGxsdX0MAACAKlejugvgLoMGDdKRI0c0adIkZWVlqUOHDlq9erXjxJDMzEwdPHjQMf/QoUN14sQJzZ49W/fcc4/q1KmjXr166fHHH6+ujwAAAOARNlNafyfKlZubq4iICOXk5Li1O/hUwVklTlojSdo1NU1hQX6T0wEAqHZVdfz2JX7TBQwAAADXEAABAAAshgAIAABgMQRAAAAAiyEAAgAAWAwBEAAAwGIIgAAAABZDAAQAALAYAiAAAIDFEAABAAAshgAIAABgMQRAAAAAiyEAAgAAWAwBEAAAwGIIgAAAABZDAAQAALAYAiAAAIDFEAABAAAshgAIAABgMQRAAAAAiyEAAgAAWAwBEAAAwGIIgAAAABZDAAQAALAYAiAAAIDFEAABAAAshgAIAABgMQRAAAAAiyEAAgAAWAwBEAAAwGIIgAAAABZDAAQAALAYAiAAAIDFEAABAAAshgAIAABgMQRAAAAAiyEAAgAAWAwBEAAAwGIIgAAAABZDAAQAALAYAiAAAIDFEAABAAAshgAIAABgMQRAAAAAiyEAAgAAWAwBEAAAwGIIgAAAABZDAAQAALAYAiAAAIDFEAABAAAshgAIAABgMX4VAOfMmaP4+HiFhIQoOTlZmzdvLnP+/Px8Pfjgg4qLi1NwcLDi4+O1YMECD5UWAACgetSo7gK4y9KlS5WRkaF58+YpOTlZTz/9tNLS0vT999+rYcOGJS4zcOBAZWdn6z//+Y+aN2+uzMxM2e12D5ccAADAs/wmAM6cOVMjR47UsGHDJEnz5s3TqlWrtGDBAo0fP77Y/KtXr9aGDRu0b98+1atXT5IUHx/vySIDAABUC7/oAi4oKNDWrVuVmprqmBYQEKDU1FRt2rSpxGXeeustderUSTNmzFCjRo3UokUL3XvvvTp9+rSnig0AAFAt/KIF8OjRoyosLFRUVJTT9KioKO3evbvEZfbt26dPP/1UISEhev3113X06FH9/e9/16+//qqFCxeWuEx+fr7y8/Md/+fm5rrvQwAAAHiIX7QAXgy73S6bzaaXX35ZXbp0Ub9+/TRz5ky9+OKLpbYCTps2TREREY5HkyZNPFxqAACAyvOLANigQQMFBgYqOzvbaXp2draio6NLXCYmJkaNGjVSRESEY1qrVq1kjNH/+3//r8RlJkyYoJycHMfj0KFD7vsQAAAAHuIXATAoKEhJSUlav369Y5rdbtf69euVkpJS4jJdu3bVL7/8opMnTzqm/fDDDwoICFDjxo1LXCY4OFjh4eFODwAAAF/jFwFQkjIyMvT888/rxRdf1HfffadRo0YpLy/PcVbwhAkTNGTIEMf8N998s+rXr69hw4Zp165d+vjjj3Xfffdp+PDhCg0Nra6PAQAAUOX84iQQSRo0aJCOHDmiSZMmKSsrSx06dNDq1asdJ4ZkZmbq4MGDjvlr1aqldevWaezYserUqZPq16+vgQMH6tFHH62ujwAAAOARNmOMqe5C+Krc3FxFREQoJyfHrd3BpwrOKnHSGknSrqlpCgvym5wOAEC1q6rjty/xmy5gAAAAuIYACAAAYDEEQAAAAIshAAIAAFgMARAAAMBiCIAAAAAWQwAEAACwGAIgAACAxRAAAQAALIYACAAAYDEEQAAAAIshAAIAAFgMARAAAMBiCIAAAAAWQwAEAACwGAIgAACAxRAAAQAALIYACAAAYDEEQAAAAIshAAIAAFgMARAAAMBiCIAAAAAWQwAEAACwGAIgAACAxRAAAQAALIYACAAAYDEEQAAAAIshAAIAAFgMARAAAMBiCIAAAAAWQwAEAACwGAIgAACAxRAAAQAALIYACAAAYDEEQAAAAIshAAIAAFgMARAAAMBiCIAAAAAWQwAEAACwGAIgAACAxRAAAQAALIYACAAAYDEEQAAAAIshAAIAAFgMARAAAMBiCIAAAAAWQwAEAACwGAIgAACAxRAAAQAALIYACAAAYDEEQAAAAIshAAIAAFiMXwXAOXPmKD4+XiEhIUpOTtbmzZtdWm7jxo2qUaOGOnToULUFBAAA8AJ+EwCXLl2qjIwMTZ48Wdu2bVP79u2Vlpamw4cPl7nc8ePHNWTIEPXu3dtDJQUAAKhefhMAZ86cqZEjR2rYsGFKTEzUvHnzFBYWpgULFpS53B133KGbb75ZKSkpHiopAABA9fKLAFhQUKCtW7cqNTXVMS0gIECpqanatGlTqcstXLhQ+/bt0+TJk116n/z8fOXm5jo9AAAAfI1fBMCjR4+qsLBQUVFRTtOjoqKUlZVV4jJ79uzR+PHjtXjxYtWoUcOl95k2bZoiIiIcjyZNmlS67AAAAJ7mFwGwogoLC3XzzTdrypQpatGihcvLTZgwQTk5OY7HoUOHqrCUAAAAVcO1pi8v16BBAwUGBio7O9tpenZ2tqKjo4vNf+LECW3ZskXbt2/XmDFjJEl2u13GGNWoUUNr165Vr169ii0XHBys4ODgqvkQAAAAHuIXLYBBQUFKSkrS+vXrHdPsdrvWr19f4skd4eHh+uabb7Rjxw7H44477lDLli21Y8cOJScne7L4AAAAHuUXLYCSlJGRofT0dHXq1EldunTR008/rby8PA0bNkzSue7bn3/+Wf/9738VEBCgNm3aOC3fsGFDhYSEFJsOAADgb/wmAA4aNEhHjhzRpEmTlJWVpQ4dOmj16tWOE0MyMzN18ODBai4lAABA9bMZY0x1F8JX5ebmKiIiQjk5OQoPD3fb654qOKvESWskSbumpiksyG9yOgAA1a6qjt++xC/GAAIAAMB1BEAAAACLIQACAABYDAEQAADAYgiAAAAAFkMABAAAsBgCIAAAgMUQAAEAACyGAAgAAGAxBEAAAACLIQACAABYDAEQAADAYgiAAAAAFkMABAAAsBgCIAAAgMUQAAEAACyGAAgAAGAxBEAAAACLIQACAABYDAEQAADAYgiAAAAAFkMABAAAsBgCIAAAgMUQAAEAACyGAAgAAGAxBEAAAACLIQACAABYDAEQAADAYgiAAAAAFkMABAAAsBgCIAAAgMUQAAEAACyGAAgAAGAxBEAAAACLIQACAABYDAEQAADAYgiAAAAAFkMABAAAsBgCIAAAgMUQAAEAACyGAAgAAGAxBEAAAACLIQACAABYDAEQAADAYgiAAAAAFkMABAAAsBgCIAAAgMUQAAEAACyGAAgAAGAxBEAAAACLIQACAABYjF8FwDlz5ig+Pl4hISFKTk7W5s2bS5135cqV6tOnjyIjIxUeHq6UlBStWbPGg6UFAACoHn4TAJcuXaqMjAxNnjxZ27ZtU/v27ZWWlqbDhw+XOP/HH3+sPn366N1339XWrVt15ZVXasCAAdq+fbuHSw4AAOBZNmOMqe5CuENycrI6d+6s2bNnS5LsdruaNGmisWPHavz48S69RuvWrTVo0CBNmjTJpflzc3MVERGhnJwchYeHX3TZL3Sq4KwSJ51rjdw1NU1hQTXc9toAAFhdVR2/fYlftAAWFBRo69atSk1NdUwLCAhQamqqNm3a5NJr2O12nThxQvXq1auqYgIAAHgFv2haOnr0qAoLCxUVFeU0PSoqSrt373bpNZ588kmdPHlSAwcOLHWe/Px85efnO/7Pzc29uAIDAABUI79oAaysV155RVOmTNGyZcvUsGHDUuebNm2aIiIiHI8mTZp4sJQAAADu4RcBsEGDBgoMDFR2drbT9OzsbEVHR5e57JIlS3Trrbdq2bJlTl3IJZkwYYJycnIcj0OHDlW67AAAAJ7mFwEwKChISUlJWr9+vWOa3W7X+vXrlZKSUupyr776qoYNG6ZXX31V/fv3L/d9goODFR4e7vQAAADwNX4xBlCSMjIylJ6erk6dOqlLly56+umnlZeXp2HDhkk613r3888/67///a+kc92+6enpmjVrlpKTk5WVlSVJCg0NVURERLV9DgAAgKrmNwFw0KBBOnLkiCZNmqSsrCx16NBBq1evdpwYkpmZqYMHDzrmnz9/vs6ePavRo0dr9OjRjunp6elatGiRp4sPAADgMX5zHcDqwHUAAQDwPVwH0E/GAAIAAMB1BEAAAACLIQACAABYDAEQAADAYgiAAAAAFkMABAAAsBgCIAAAgMUQAAEAACyGAAgAAGAxBEAAAACLIQACAABYDAEQAADAYgiAAAAAFkMABAAAsBgCIAAAgMUQAAEAACyGAAgAAGAxBEAAAACLIQACAABYDAEQAADAYgiAAAAAFlOjuguAEhij0IIz5/7Oy5N+52sCAFhUWJhks1V3KfwOycIbnTql75668dzfT1VvUQAAqFYnT0o1a1Z3KfwOXcAAAAAWQwugNwoLU6u7V0iStj6UqrAgvqbzFdqNthw4piMn8xVZK1id4uspMIDuAaAs677N0j/f+05ZOfmOadERwZr451bq0zq6GksGlCMsrLpL4JdIFt7IZtPpoJBzf9esKREAHVbvzNSUt3cpM+eMY1pMRIgmD0jUVW1iqrFkgPdavTNTo1bulpFNKtq3SDpwWrpt5W7NDQtj+wEshi5g+IzVOzM1avE2p/AnSVk5ZzRq8Tat3plZTSUDvFeh3WjK27tkSniuaNqUt3ep0F7SHAD8FQEQPoGDGHBxNu8/VuxH0/mMpMycM9q8/5jnCgWg2hEA4RM4iAEX5/CJ0rebi5kPgH9gcBl8Agcx4OI0rB1S/kwVmA+eU2g32rz/mA6fOKOGtUPUJYET3uA+BED4BCscxNjZoyp0SainmIgQZeWcKXEIhU1SdMS59Q3egxPeUNUIgPAJ/n4QY2ePqhIYYNPkAYkatXibbJLT9lP082LygES//7HhSz+wik54u3BfV3TC29y/dmS/gEpjDCB8QtFBTPrfQauIrx/EOLsZVe2qNjGa+9eOahge7DQ9OiLEEmFi9c5MdXv8A930/Oe6a8kO3fT85+r2+AdeuW1xwhs8hQAIn+GPBzF29vCUq9rE6P2Mno7/Fw3rrE8f6OWT201F+NoPLE54g6cQAOFT/O0gxs7eOxXajTbt/VVv7vhZm/b+6jcB/PwWcm/uAnUXX/yBxQlv8BTGAMLn+NNBjJ2992E8pv+oyA+slGb1PVewMnjzCW++NI4S5SMAAtXIm3f2VsTge//iiz+wvPWEN34Y+R+6gIFqVLSzL+03tE3ndrK+enazL/HF7kKUzRd/YHnjCW++No4SriEAAtXIG3f2VsV4TP/jqz+wvOmEN34Y+S8CIFDNvGlnb2W+2F2IsvnyDyxvOeGNH0b+izGA8Eu+Nlj5qjYx6tq8gdo+vFbSuZ1990sjvbrM/sYXuwu9mbu2wcq+TtEPrMlvfavs3HzH9OgSxq95237DG05444eR/yIAwu/46mBlT+7sve1A5w28dfC9L3LXNuiu13HlB5av7jeqGj+M/BddwPArDFYuny/dFcGTfLm70Ju4axt097Zc1g8s9hul89VxlCgfAdDi/OmCtwxWLh8HurIxHrNy3LUNenJbZr9RNn4Y+S+6gC3M1S4PX+ku9MWLvnpSeQc6m84d6PokRnvl9+spjMe8eO7aBj25LbPfKF9FxlHCdxAALcrVC956elxMZcImg5XL5usHOk/+EPGGwfe+yF3boCe35Yq+l6/8IHY3fhj5HwKgBbnaEmS3S6Nf8dxdESobNhmsXDZfDsgM0PcN7toGPbktV+S9rL4e8sPIvzAG0IJcbQn6x5s7PTYuxh1j0xisXLaKHlS9ZXwo4xZ9h7u2QU9uy66+1295BayHLvCW/QbKRwC0IFdbeI7lFZT6nDsv/umuQdgMVi5bRQ6q3nKmMAP0fYu7tkFPbsuuvNdD/VvpkVWsh+Xxlv0GXEMAtCB3doG6o7vQnVea5yzO0rl6UF23K8trWjoqum54W+uDt5XHE9y1DXpyWy7vverWDOZuGOWgpd73MAbQgly54G3dmpfoWN7v5b6WO8Kku8emMVi5dOWdzdcnMVrdHv/Aa84Ursi64W3js7ytPJ7krm3Qk9tyWe/15o6fXXoNbxw/6wlcYcA30QJoQa60BD16bRuPjcGpigHfnr6rhi+18pR1j1Fvu++nq9/5gaOnvKr1wd2tIb62jknu2wY9uS2X9l6cYFY2b9tvwDV+FQDnzJmj+Ph4hYSEKDk5WZs3by5z/o8++kgdO3ZUcHCwmjdvrkWLFnmmoF6gvC6Pfu1iPTYGx5dP3vDVMS+lHei87UxhV9aN6PBgvbr5oNeMz3L3uEVX1zFfDIm+wpf3UZ7gbfsNuMZvAuDSpUuVkZGhyZMna9u2bWrfvr3S0tJ0+PDhEuffv3+/+vfvryuvvFI7duzQuHHjdOutt2rNmjUeLnn1KaslqOh5T4zB8dWTN/xxzIu3tXS4sm7c1OUPysr1ntYHd7aGuLqO+eoPEV/hq/soT/G2/QZc4zdjAGfOnKmRI0dq2LBhkqR58+Zp1apVWrBggcaPH19s/nnz5ikhIUH/+te/JEmtWrXSp59+qqeeekppaWkeLfuFjDEKPntufJb91CnZz1bd12QrOOt4r05RIbKdOS37ec/3bRqhlFGd1eWx9ZKk5/6WpK7NGigwwCb7qVNuK0ffphGad2MrPbrqOx0+cd7YtPAQTex3mfo0jXC8n/28MpdWP67MUxmFdqNpK7cr6Gx+ic/bJE1buV2948NdPihUdZldea9OUSGKC7MpO7f08aFR4SHqFBXi1u+/LOWtG/ln7Y7PUpYjR36TPSbUpfeszHdx5MhvbimPq+uYOXVady/bISPp/J9qv/2ar3GLNmnW4A7qkxh97rN4wTrmza9T1jwV2Ue5iye/r8qUp6r3G7bQUNls1gzXVclmjPH5foKCggKFhYVpxYoVuu666xzT09PTdfz4cb355pvFlunRo4c6duyop59+2jFt4cKFGjdunHJyckp8n/z8fOXn/2/Dz83NVZMmTZSTk6Pw8HC3fZ6Tx3N16E/Jbns9AAB8VcttWxUQFubW18zNzVVERITbj9++xC+6gI8eParCwkJFRUU5TY+KilJWVlaJy2RlZZU4f25urk6fPl3iMtOmTVNERITj0aRJE/d8gAuEBflNwywAAJVyquBsdRfBL5E0KmDChAnKyMhw/F/UAuhuttBQtdy2tcx5ThWcVdKj70uStv4jtcTQ6Mo87uJt5XFFZcr8xf5jGrqw7JOMJGnRsC5KTqjnts/uyXoutBtt+ek3HTlxRpG1Q9Qprm6x7mx3laeyZV63K0t3LdkhSU5dUEWlPb8b1BPfhTvK4+o65oonbmynq9vFujSvJ9cxb3sdd3Fl3biw662kdaOy7+XueVxRFfuNbaGuDd1AxfhFAGzQoIECAwOVnZ3tND07O1vR0SVvSNHR0SXOHx4ertBSVrbg4GAFBweX+Jw72Ww22cpp7g6ocVb5Nc6VJSAsTAElbECuzOMuJuB3x3ttyT5T4rW6PFkeV1SmDru0ClW9+hFlXksxOiJEXVo1UkCAzW2f3ZP1HCAppXXNsudx03pY2TKndWqqp0NCS73uXtp5Jyy5rX7KeB13lMeVdczV63VGRtZ1uQvNk/sWb3sddymtPIV2o4fX7deZGiUfR2ySHl63X6kdE1weO+wt26DjdeT+/Qbj/6qGXwTAoKAgJSUlaf369Y4xgHa7XevXr9eYMWNKXCYlJUXvvvuu07R169YpJSWlqovrd1bvzNTkt751/D904Zd+f8HborMCRy3eJptKbuVx91mBVqzniriqTYz6JEZr8/5jOnzijBrWDqnWG9a7Wp7zL9eyef8xR6h3ZR179No2emTVd+X/ELHo5Um8TUXOEE9pVt9zBYMl+cUYQEnKyMjQ888/rxdffFHfffedRo0apby8PMdZwRMmTNCQIUMc899xxx3at2+f7r//fu3evVvPPvusli1bprvvvru6PoJPKrpMxfl3lZB8+1Io57vw4Hz+/0WXyYmOcL60QVXcqsrf69ldAgNsSmlWX9d2aKSUZvWr/bIc5ZVn9c5Mpc7c4Ph/6MIvnS7fUt465snrdVaFsrYvX1ba5+J6efAmftECKEmDBg3SkSNHNGnSJGVlZalDhw5avXq140SPzMxMHTx40DF/QkKCVq1apbvvvluzZs1S48aN9cILL1T7JWB8ib/f/seVFjdPtDr5ez37qtJa7lxVFOov/F6LQn3Rj4jy1rGikHhhd3O0l7cO+2uLdlmfi+vlwZv4TQCUpDFjxpTa5VvSXT6uuOIKbd++vYpL5b/8uTvD1YOz9L9Wnqriz/XsqyobXioa6stbx7yt+7s8Fdm+fEl5n2vOzX8s9z7sdNnDU/ymCxieV9HuDF/p7nH3rbwqi24j7+KO7viquHeqJ7u/K7Mte9v25S6ufK5HVn2nh/q7t8veV/ar5/PFMvsjAqCP8oYNqCLdGeWNdfIm3nZjc2/uNvKG9dCT3BVefDnUV3Zb9rbty11c/Vx1awa5beywq9+FN22nvnQs8HcEQB/kLRuQqzdI/y2vwKdOYPC2g7O33ojeW9ZDT3JXePHmUF8Wd7R+etv25S4V+VxXtYnRpw/00qsj/6RZgzvo1ZF/croPuytc/S68aTvlZDbvQgD0Md60Ablyg/SH+rfSI6t8q7vH2w7O3ngjem9aDz3JXeHFW0N9WdzV+ult25e7VPRzVabL3tXv4t2vXd9Oq7qV0F+7/n0ZAdCHeOMGVN5lKurWDPa57h5vPDh78pIz5fHG9dBT3BVevDHUFyktCLir9bMqti9v6OL05H7D1e/iH2/udGk79UQrob92/fsyvzoL2N9569mgZZ2B+OaOn116DW/q7qmKizxX9pIhkvec6emt66EnFB3k3XEWpzdevqWss5vzz9pdeo3ytmV3b1/ecjkZT14c3tX95bG8glKfK9pOZ3/wo55+/4cqPyPbX7v+fRktgD7Emzeg0rozfLW7x50tbu78de0NFzquivXQG1pwXOHuljt3jAVzl/K69Q8czXPpdVzZlt21fXnbUARPtdS7c3+5cON+j7Tm++qxwJ/RAuhDfHEDcmeLiae5o8XNH6935u710FtacFzl7pa7qr6OpCtcuS7hq5sPKjo8RNm57tmWK7t9eesF0j3RUu/KftXV+0QfP136PO5szfflY4G/ogXQh3jj2LTyePNYJ1d4YqB2VQy2LlIVrWnuXA+9rQXHVd7UcucOrnTrZ+Xm66Yuf5Dkvm25MtuXN48pq+qWelf2q49e26bc7bRO6CUuvZ87epV8/VjgjwiAPsRXNyBvOoHhfFUdlKrjAOWJwdwVXQ9Lq2dfP5nEG7rj3cXVA3x8gzCv2Za9eUiMJ7jjPtHDusa79F7u6lWqyLHAV4aF+DK6gH2MNw4cd4W3nMBQxBPdjp4+QHmyu9nV9bCseo4IDaqWk0nccUKOv6lIt35Ks/pesS374pAYd6vsfaL7JEZryZeHPNot68qxwNeGhfgqAqAP8rYw5SpvGOskeS4oefIAVR3jocpbD8ur5+Eutj64swWHA0vJKjo+yxu2ZcaUnVPZ+0R76sxlV8vsj+OmvRVdwD7Kn7qfPMmT3Y7eeF0wd4+HKm09dKWeX3fxEkHuasHx1fGGnuCLw0t8sczVpazjhTcN0fH1YSG+hgAIS/FkUPLkAcrbxkO5Us/H8n5XvZpBHgnIHFjK501BwFW+WGZv5C0nNXnziT3+iC5gWIqng5Knxmx623goV+vvug6xWrjxQJV3P1n54tUV4YvDS3yxzN7IG7r1ve2HrL8jAMJSqiMoect1wTw5HsrV+uuTGK0uCfWqPCBzYHGdNwSBivLFMqM4b/sh6+8IgLCU6gpKVX2A8uRtqFxRkXoODLBVeUDmwAJ4P2/7IevvGAMIS/HngePeNB6qovVc1Sc1+eJF1AGr8ef9szeyGWOsO+q5knJzcxUREaGcnByFh4dXd3GKOVVwVomT1kiSdk1NU1gQDb5FVu/MLNbt6C+XAym0G68ZD+VN9Vx0FrBUcgspJw0A3sET+w1vP357AgGwErx9BSIAls2bgpI/86Z69qZACqB0Vb3f8PbjtyeQCGBZDBz3DG+qZ84YBXyDN+03/BUBEIClcGABAE4C8WvcTBsAAJSEAOinVu/MVOrMDY7/hy78Ut0e/8DSt7sCAADn0AXsjYyRTp266MXXfZuljCU7ZCSFnjc958gZZSz4TIGDO6hP6+hKFxMAgCoXFibZGKfrbgRAb3TqlFSr1kUv3kfSrrJmeOqiXxoAAM86eVKqWbO6S+F36AIGAACwGFoAvVFY2LlfPBfhna9/0X3Lvy53vif+0k5Xt4u9qPcAAMBjwsKquwR+iQDojWy2i27urt+wnk4HlX8/0/oN69GkDgCARdEF7Ge45ykAACgPAdDPcDNtAABQHgKgH7qqTYzm/rWjoiOcu4KjI0K44T0AAGAMoL/inqcAAKA0BEA/xj1PAQBASQiAlWDMuXvr5ubmVnNJAACAq4qO20XHcSsiAFbCiRMnJElNmjSp5pIAAICKOnHihCIiIqq7GNXCZqwcfyvJbrfrl19+Ue3atWVz830Kc3Nz1aRJEx06dEjh4eFufW38D/XsGdSzZ1DPnkE9e0ZV1rMxRidOnFBsbKwCAqx5PiwtgJUQEBCgxo0bV+l7hIeHs4PxAOrZM6hnz6CePYN69oyqqmertvwVsWbsBQAAsDACIAAAgMUQAL1UcHCwJk+erODg4Oouil+jnj2DevYM6tkzqGfPoJ6rFieBAAAAWAwtgAAAABZDAAQAALAYAiAAAIDFEAABAAAshgDohebMmaP4+HiFhIQoOTlZmzdvru4i+bSPP/5YAwYMUGxsrGw2m9544w2n540xmjRpkmJiYhQaGqrU1FTt2bOnegrrw6ZNm6bOnTurdu3aatiwoa677jp9//33TvNQ15U3d+5ctWvXznFx3JSUFL333nuO56njqjF9+nTZbDaNGzfOMY26do+HH35YNpvN6XHZZZc5nqeeqwYB0MssXbpUGRkZmjx5srZt26b27dsrLS1Nhw8fru6i+ay8vDy1b99ec+bMKfH5GTNm6N///rfmzZunL774QjVr1lRaWprOnDnj4ZL6tg0bNmj06NH6/PPPtW7dOv3+++/q27ev8vLyHPNQ15XXuHFjTZ8+XVu3btWWLVvUq1cvXXvttfr2228lUcdV4csvv9Rzzz2ndu3aOU2nrt2ndevWyszMdDw+/fRTx3PUcxUx8CpdunQxo0ePdvxfWFhoYmNjzbRp06qxVP5Dknn99dcd/9vtdhMdHW2eeOIJx7Tjx4+b4OBg8+qrr1ZDCf3H4cOHjSSzYcMGYwx1XZXq1q1rXnjhBeq4Cpw4ccJceumlZt26daZnz57mrrvuMsawPrvT5MmTTfv27Ut8jnquOrQAepGCggJt3bpVqampjmkBAQFKTU3Vpk2bqrFk/mv//v3KyspyqvOIiAglJydT55WUk5MjSapXr54k6roqFBYWasmSJcrLy1NKSgp1XAVGjx6t/v37O9WpxPrsbnv27FFsbKyaNm2qW265RQcPHpREPVelGtVdAPzP0aNHVVhYqKioKKfpUVFR2r17dzWVyr9lZWVJUol1XvQcKs5ut2vcuHHq2rWr2rRpI4m6dqdvvvlGKSkpOnPmjGrVqqXXX39diYmJ+uyzzyRRx+6yZMkSbdu2TV9++WWx51if3Sc5OVmLFi1Sy5YtlZmZqSlTpqh79+7auXMn9VyFCIAA3G706NHauXOn0zgeuE/Lli21Y8cO5eTkaMWKFUpPT9eGDRuqu1h+5dChQ7rrrru0bt06hYSEVHdx/Nqf//xnx9/t2rVTcnKy4uLitGzZMrVq1aoaS+bf6AL2Ig0aNFBgYKCys7OdpmdnZys6OrqaSuXfiuqVOnefMWPG6J133tGHH36oxo0bO6ZT1+4TFBSk5s2bKykpSdOmTVP79u01a9Ys6tiNtm7dqsOHD6tjx46qUaOGatSooQ0bNujf//63atSo4WiRoq7dr06dOmrRooV+/PFH1ukqRAD0IkFBQUpKStL69esd0+x2u9avX6+UlJRqLJn/SkhIUHR0tFOd5+bm6osvvqDOK8gYozFjxuj111/XBx98oISEBKfnqeuqY7fblZ+fTx27Ue/evfXNN99ox44djkenTp10yy23aMeOHWratCl1XUVOnjypvXv3KiYmhnW6KlX3WShwtmTJEhMcHGwWLVpkdu3aZW677TZTp04dk5WVVd1F81knTpww27dvN9u3bzeSzMyZM8327dvNTz/9ZIwxZvr06aZOnTrmzTffNF9//bW59tprTUJCgjl9+nQ1l9y3jBo1ykRERJiPPvrIZGZmOh6nTp1yzENdV9748ePNhg0bzP79+83XX39txo8fb2w2m1m7dq0xhjquSuefBWwMde0u99xzj/noo4/M/v37zcaNG01qaqpp0KCBOXz4sDGGeq4qBEAv9Mwzz5g//OEPJigoyHTp0sV8/vnn1V0kn/bhhx8aScUe6enpxphzlxl46KGHTFRUlAkODja9e/c233//ffUW2geVVMeSzMKFCx3zUNeVN3z4cBMXF2eCgoJMZGSk6d27tyP8GUMdV6ULAyB17R6DBg0yMTExJigoyDRq1MgMGjTI/Pjjj47nqeeqYTPGmOppewQAAEB1YAwgAACAxRAAAQAALIYACAAAYDEEQAAAAIshAAIAAFgMARAAAMBiCIAAAAAWQwAEAACwGAIgAACAxRAAAQAALIYACAAAYDEEQAAAAIshAAIAAFgMARAAAMBiCIAAAAAWQwAEAACwGAIgAACAxRAAAQAALIYACAAAYDEEQAAAAIshAAIAAFgMARAAAMBiCIAAAAAWQwAEAACwGAIgAACAxRAAAQAALIYACAAAYDEEQAAAAIshAAIAAFgMARAAAMBiCIAAAAAW8/8BIHGc/R2AuSYAAAAASUVORK5CYII="
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Except at zero lag, the sample autocorrelation values lie within the 99%-confidence bounds for the autocorrelation of a white noise sequence. From this, you can conclude that the residuals are white noise. More specifically, you cannot reject that the residuals are a realization of a white noise process.\n",
        "\n",
        "除零延时外，样本自相关值在白噪声序列自相关的99%置信范围内。由此可以得出结论，残差是白噪声。更具体地说，无法拒绝残差是一个白噪声过程的假设。"
      ],
      "metadata": {
        "id": "hrJx5S_F5Q2n"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Create a signal consisting of a sine wave plus noise. The data are sampled at 1 kHz. The frequency of the sine wave is 100 Hz. Set the random number generator to the default settings for reproducible results.\n",
        "\n",
        "创建一个由正弦波和噪声组成的信号。数据采样频率为1 kHz。 正弦波的频率为100hz。 将随机数生成器设置为可重现结果的默认设置。"
      ],
      "metadata": {
        "id": "RAeXwHRZWhnX"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "fs = 1000\n",
        "t = np.arange(0, 1-1/fs, 1/fs)\n",
        "x = np.cos(2* np.pi * 100 * t) + np.random.randn(len(t))"
      ],
      "metadata": {
        "trusted": true,
        "id": "E4f8DN2K5Q2n"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Use the discrete Fourier transform (DFT) to obtain the least-squares fit to the sine wave at 100 Hz. The least-squares estimate of the amplitude is 2 / N times the DFT coefficient corresponding to 100 Hz, where N is the length of the signal. The real part is the amplitude of a cosine at 100 Hz and the imaginary part is the amplitude of a sine at 100 Hz. The least-squares fit is the sum of the cosine and sine with the correct amplitude. In this example, DFT bin 101 corresponds to 100 Hz.\n",
        "\n",
        "使用离散傅里叶变换（DFT）获得100Hz的最小二乘拟合正弦波。复制的最小二乘估计为2/N乘以100Hz所对应的DFT系数，其中N为信号长度。实部是信号在余弦信号100Hz的振幅，虚部是正弦信号在100Hz处的振幅，最小二乘拟合是相应正确振幅的余弦与正弦信号之和。本例中，DFT的第101维对应100Hz"
      ],
      "metadata": {
        "id": "4Sqhlp7b5Q2o"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "xdft = fft(x)\n",
        "ampest = 2 / len(x) * xdft[100]\n",
        "xfit = ampest.real * np.cos(2 * np.pi * 100 * t) + ampest.imag * np.sin(2 * np.pi * 100 * t)"
      ],
      "metadata": {
        "trusted": true,
        "id": "sUIkx76B5Q2o"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "plt.plot(t, x, 'b')\n",
        "plt.plot(t, xfit, 'r')\n",
        "plt.axis([0, 0.30, -4, 4])\n",
        "plt.xlabel('Seconds')\n",
        "plt.ylabel('Amplitude')\n",
        "plt.show()"
      ],
      "metadata": {
        "trusted": true,
        "id": "Q2WU8XAh5Q2p",
        "outputId": "f6a584f3-2b2a-496c-982f-45585145d674"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": "<pyolite.display.Image at 0x3d3bdf8>",
            "image/png": 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"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "residuals = x - xfit\n",
        "xc,lags = autocorrelation(residuals, 50);"
      ],
      "metadata": {
        "trusted": true,
        "id": "AJE1VqX95Q2p"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "lconf = -conf99 / np.sqrt(len(x))\n",
        "hconf = conf99 / np.sqrt(len(x))\n",
        "lline = lconf * np.ones(len(lags))\n",
        "hline = hconf * np.ones(len(lags))"
      ],
      "metadata": {
        "trusted": true,
        "id": "983g-Yua5Q2p"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "plt.stem(lags, xc)\n",
        "plt.ylim([lconf-0.03, 1.05])\n",
        "plt.plot(lags, lline, 'r')\n",
        "plt.plot(lags, hline, 'r')\n",
        "plt.title('Sample Autocorrelation with 99% Confidence Intervals')\n",
        "plt.show()"
      ],
      "metadata": {
        "trusted": true,
        "id": "admCJRnk5Q2p",
        "outputId": "011ffdd9-b134-40e6-8f6f-dd8087cb6233"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": "<pyolite.display.Image at 0x3fdb230>",
            "image/png": 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"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Again, you see that except at zero lag, the sample autocorrelation values lie within the 99%-confidence bounds for the autocorrelation of a white noise sequence. From this, you can conclude that the residuals are white noise. More specifically, you cannot reject that the residuals are a realization of a white noise process.\n",
        "\n",
        "同样的可以看到，除了零延迟外，样本自相关值位于白噪声序列99%自相关的置信范围内。由此可以得到结论，残差为白噪声，无法拒绝残差是白噪声过程的实现的假设。"
      ],
      "metadata": {
        "id": "_xqADj3C5Q2p"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Finally, add another sine wave with a frequency of 200 Hz and an amplitude of 3/4. Fit only the sine wave at 100 Hz and find the sample autocorrelation of the residuals.\n",
        "\n",
        "最后，我们加入一个频率为200Hz，振幅为3/4的正弦波，只拟合100Hz的正弦波，求残差的样本自相关。"
      ],
      "metadata": {
        "id": "TyZ62ng7euV6"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "x = x + 3/4 * np.sin(2 * np.pi * 200 * t)\n",
        "xdft = fft(x)\n",
        "ampest = 2 / len(x) * xdft[100]\n",
        "xfit = ampest.real * np.cos(2 * np.pi * 100 * t) + ampest.imag * np.sin(2 * np.pi * 100 * t)\n",
        "residuals = x - xfit\n",
        "xc,lags = autocorrelation(residuals, 50);"
      ],
      "metadata": {
        "trusted": true,
        "id": "rMjTgAyG5Q2q"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Plot the sample autocorrelation along with the 99%-confidence intervals.\n",
        "\n",
        "绘制样本自相关图及99%置信区间。"
      ],
      "metadata": {
        "id": "m4kZsAGJ5Q2q"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "plt.stem(lags, xc)\n",
        "plt.ylim([lconf-0.12, 1.05])\n",
        "plt.plot(lags, lline, 'r')\n",
        "plt.plot(lags, hline, 'r')\n",
        "plt.title('Sample Autocorrelation with 99% Confidence Intervals')\n",
        "plt.show()"
      ],
      "metadata": {
        "trusted": true,
        "id": "TNWWCsuo5Q2q",
        "outputId": "4c160f7e-c088-468f-bb8f-3f5e3dd1f14f"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": "<pyolite.display.Image at 0x3d7d338>",
            "image/png": 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"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "In this case, the autocorrelation values clearly exceed the 99%-confidence bounds for a white noise autocorrelation at many lags. Here you can reject the hypothesis that the residuals are a white noise sequence. The implication is that the model has not accounted for all the signal and therefore the residuals consist of signal plus noise.\n",
        "\n",
        "在这种情况下，自相关值在很多滞后点明显超过了99%的置信区间。这里可以拒绝残差是白噪声序列的假设。这意味着模型没有考虑到所有的信号，因此残差由信号加噪声组成。"
      ],
      "metadata": {
        "id": "A3H8JZQ25Q2q"
      }
    },
    {
      "cell_type": "code",
      "source": [
        ""
      ],
      "metadata": {
        "id": "B1QkhUfm5Q2r"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}